Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.
Keywords: crossed modules, homotopy 2types, generalised van Kampen Theo rem, crossed resolution, Postnikov invariant.
AMS Classification (1991): 18G10, 20F38, 55P15, 55Q20.
Theory and Applications of Categories, Vol. 1, 1995, No. 3, pp 54-71.
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